Q4. *(i) m & n are two integers such
that m=n ^{2}-n. Show that m^{2}-2m
is divisible by 24.*

*(ii) If x & y are two
positive numbers such that x + y = 1, find maximum value of x ^{4}y + xy^{4}.*

**Solution :**

**(i)** m = n^{2}-n (Given)

So, m^{2}
– 2m = n^{2}(n-1)^{2 }- 2n(n-1)

=
n(n-1)[ n^{2} – n – 2]

= n(n-1)(n-2)(n+1)

=(n-2)(n-1)n(n+1) …
Product of 4 consecutive integers

We know that
product of any four consecutive integer is divisible by 4 !

Thus, m^{2}-2m
is divisible by 24.

**(ii) solution is : HERE **